Basic definitions and theorems dealing with spline functions are presented. Geometrical interpretation of such functions is also shown. Constructions of cubic spline functions with different boundary conditions are presented. The examples show the most interesting properties of the spline functions. Particular attention was paid to the high order of convergence both in the rase of the interpolation of the given functions and the approximation of their first derivatives. The analysis carried out shows strong connection between the assumed boundary conditions and the convergence of the spline functions. It has been stated that the boundary condition of the type of gamma＇, the most frequently used, leads to the function burdened with the biggest error.